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Unformatted text preview: 2- Calculating the dead time for all process steps Time = Distance / chart Speed Sample calculation: From the chart, dead time for (+)ve step change for 1st tank = 0.3 cm Dead time = 0.3 cm / (2 cm / min) = 0.15 min. 3- All the readings are converted to concentration by using the calibration curve (Fig 3 page PC1-9) and the results are recorded in tables. 4- The time constant of the 1st tank by plotting Ln (1-C1`/A) vs. (t) -1/τ = slope = -0.5478 τ = 1.825 min 5- Time constants (theoretically): V1 = πr2 h1 = π (8.5) 2 (11.15) = 0.633 ml V2 = πr2 h2 = π (8.5) 2 (11.00) = 0.624 ml vo1 = vo2 = 0.2 lit/min for a step input τ1= V/vo1 = 3.164 min (for first tank) τ2= V/vo2 = 3.121 min (for second tank) 6- Comparison of theoretical and experimental values of time constants for the first tank: % Error = (3.164-1.825)/3.164 * 100 = 42.3%. 7- Plot and comparison C1`(t) vs. time both exp. and theore. For step change response of first tank theoretical:
− t 1 −e τ1 ′ C1(t ) = A 12 8- Plot and comparison C2`(t) vs. time both exp. and theo. For step change response of second tank theoretical:
−t −t 1 + τ 1 e τ1 + τ 2 e τ 2 ′ C2 ( t ) = A τ 2 − τ1 τ1 − τ 2 13 ...
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- Fall '08
- Derivative, Calculation, dead time, step change response